This issue may have been reported several times, and it may not even be a bug, but rather intended. This is a big annoyance and is super illogical and it needs to be addressed.

When putting a mob in a minecart and putting them on a regular rail, the mob is able to assert control over the cart and make it move. They are also able to resist power rails and unpowered rails.

There is no reason for them to be able to do that. If a powered rail is telling the minecart to go, it should go. It shouldn't be dictated by whatever creature is in the cart, including players.

Steps to reproduce:
1: Put a villager in a minecart on a regular rail.
2: Watch as the villager decides where it actually goes, even though the cart shouldn't be moving period.

This is completely illogical and very counterintuitive, as the main reason for putting mobs in minecarts is to control exactly where they go. It's unbelievably frustrating trying to sort mobs using minecarts when they fight against the powered rails and end up not moving.

This is an opinion shared between myself and several peers and we would like to see it addressed as soon as possible.